Furthermore, the \(\alpha \)  decay process is also a low-energy phenomenon, and it can not actually cause a sensible variation in the ground-state properties of an alpha emitter[1]}, [2]}. On the other hand, it is shown that an \(\alpha \)  cluster is mostly formed in the pre-surface region of the nucleus. Some sensible density overlapping between alpha and daughter nuclei in more dense regions due to the considering the effect of Pauli blocking from the saturated core density [3]}. Therefore, the interior regions of the interaction potentials between alpha and daughter nuclei would be affected by the PEP, where the tunnelling process occurs. One of the possible mechanism that is extensively being used for simultaneously applying the PEP and clusterization state in the dinuclear system is the renormalizing the strength of effective NN interaction due to the Bohr-Sommerfeld (BS) quantization condition [4]}, [5]}, [6]}, [7]}, [8]}, [9]}, [10]}. This procedure compensates for the deficiency of the PEP in the DF formalism to some extent.
